stable crystalline phosphorus ylides are obtained in excellent yields from the 1:1:1 addition reactionbetween hydantoins or thiohydantoins and dialkyl acetylenedicarboxylates in the presence oftriphenylphosphine. these phosphoranes undergo smooth intramolecular wittig reaction followedby an electrocyclic ring opening to produce dialkyl (e)-2-(2,5-dihydro-5,5-diaryl-2-thioxo-1h-imidazol-4-yl)fum...

Restricted rotation distance between pairs of rooted binary trees quantifies differences in tree shape. Cleary exhibited a linear upper bound of 12n for the restricted rotation distance between two trees with n interior nodes, and a lower bound of (n − 1)/3 if the two trees satisfy a reduction condition. We obtain a significantly improved sharp upper bound of 4n− 8 for restricted rotation dista...

Restricted rotation distance between pairs of rooted binary trees measures differences in tree shape and is related to rotation distance. In restricted rotation distance, the rotations used to transform the trees are allowed to be only of two types. Restricted rotation distance is larger than rotation distance, since there are only two permissible locations to rotate, but is much easier to comp...

Introduction: Cervical spine abnormalities can affect the ear vessels and or nerves with different mechanisms. Ear dysfunctions following cervical spine injuries can be manifested as hearing loss, vertigo, or tinnitus. Usually, cervical spine injuries can cause pain and Range of Motion (ROM) limitation. The major objective of this study was to determine which cervical ROM limitation was accompa...